Medan
Reputation
Top tag
Next privilege 100 Rep.
Edit community wikis
 Feb6 comment independent variables or not @DilipSarwate: I think they are Normal and independent in fact. Although I am not sure why the sum and difference are independent in that case. If $X$ and $Y$ are normal and indpnt, then $X+Y$ is also normal, so as $X-Y$, why the last two are independent then? Feb6 accepted Is $X_t$ a martingale? Feb6 comment independent variables or not @DilipSarwate: from aboove I see the statement is in fact incorrect, would that make a difference if $X$ and $Y$ are iid? Feb6 asked independent variables or not Feb6 comment Is $X_t$ a martingale? I see, thanks. I would guess because they both involve the information at time $u$, so they overlap there and not independent? Then, second part ends up being $\int_u^t E[W_s/F_u]ds=W_u(t-u)$? And clearly this is not zero and therefore it is not a martingale? Feb6 revised Is $X_t$ a martingale? added 52 characters in body Feb6 revised Is $X_t$ a martingale? deleted 53 characters in body Feb6 asked Is $X_t$ a martingale? Oct31 awarded Popular Question Sep11 awarded Popular Question Jul2 awarded Curious Apr17 asked difference of the values of a function is an integral Oct28 awarded Nice Question Apr21 asked relation between Holder continuous and weakly differentiable for the coefficients of a pde Apr17 revised matrix with distinct bounded eigen values is bounded? added 75 characters in body Apr16 revised matrix with distinct bounded eigen values is bounded? added 614 characters in body Apr15 asked matrix with distinct bounded eigen values is bounded? Mar22 revised Existence of the degenerate elliptic PDE coefficient condition added 603 characters in body Mar11 comment Existence of the degenerate elliptic PDE coefficient condition ok, but the condition saying $c \leq c_0 <0$ doesn't make sense to me. First, consider a backward pde $v_t+v_{xx}=0$, which doesn't satisfy that condition. But having a change of variables as $u:=e^{ct}v,c<0$ I have an equation for $u$: $u_t+u_{xx}-cu=0$ which satisfies the condition and then there is existence. But the two equations are equivalent up to a change of variables so they both either have it or not. Another argument, we trivially know that heat equation, can be viewed as a degenerate elliptic equation and has a solution but does't not satisfy the property of having $c\leq c_0<0$. Mar11 comment Existence of the degenerate elliptic PDE coefficient condition So, coefficient $c$ affects coercivity? Isn't it a property of the coefficint in front of the second order operator? I have looked at your answer, I don't think it is related to my question as I rather have issues with understanding of the existence of the solutions to the basic elliptic and parabolic equations, just don't have any other book on parabolic equations at hands right now.